The direct conversion of $A$ to $B$ is difficult, hence it is carried out by the following shown path.
Given $\Delta S_{(A \rightarrow C)}=50 \mathrm{eu}, \quad \Delta S_{(C \rightarrow D)}=30 \mathrm{eu}, \quad \Delta S_{(B \rightarrow D)}=20 \mathrm{eu}$ where eu is entropy unit, then $\Delta S_{(A \rightarrow B)}$ is

• A

  $+100 \mathrm{eu}$
• Correct answer
  B

  $+60 \mathrm{eu}$
• C

  $-100 \mathrm{eu}$
• D

  $-60$ eu

Solution

Given: $\quad \Delta S_{(A \rightarrow C)}=50 \mathrm{eu}, \Delta S_{(C \rightarrow D)}=30 \mathrm{eu}, \Delta S_{(B \rightarrow D)}=20 \mathrm{eu}$ where eu is entropy unit. $$ \text { Therefore, } \begin{aligned} \Delta S_{(A \rightarrow B)} & =\Delta S_{(A \rightarrow C)}+\Delta S_{(C \rightarrow D)}+\Delta S_{(D \rightarrow B)} \\ & =\Delta S_{(A \rightarrow C)}+\Delta S_{(C \rightarrow D)}-\Delta S_{(B \rightarrow D)} \\ & =50+30-20=60 \mathrm{eu} \end{aligned} $$

Hence, the correct answer is option: 'B'.